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Precalculus · Complex-Numbers

Polar form of 3I

3 i

Step by step

  1. z = 3 i = 0 + (3)i

    Read off the real and imaginary parts.

  2. |z| = \sqrt{0^2 + 3^2} = 3

    The modulus is the distance from the origin (Pythagoras).

  3. \theta = \arg z = \frac{\pi}{2} \approx 1.5708

    The argument is the angle from the positive real axis (watch the quadrant).

  4. z = 3\left(\cos \frac{\pi}{2} + i\sin \frac{\pi}{2}\right) = 3 e^{i \frac{\pi}{2}}

    Polar and exponential forms (Euler).

Reveal the answer
3 e^{i \frac{\pi}{2}}